# How do you list all possible roots and find all factors and zeroes of #5x^3+29x^2+19x-5#?

##### 1 Answer

Jun 23, 2016

with zeros

#### Explanation:

#f(x) = 5x^3+29x^2+19x-5#

Note that if you reverse the signs on the terms of odd degree then the sum of the coefficients is

That is:

Hence

#5x^3+29x^2+19x-5 = (x+1)(5x^2+24x-5)#

To factor the remaining quadratic use an AC method:

Look for a pair of factors of

The pair

Use this pair to split the middle term and factor by grouping:

#5x^2+24x-5#

#=5x^2+25x-x-5#

#=(5x^2+25x)-(x+5)#

#=5x(x+5)-1(x+5)#

#=(5x-1)(x+5)#

Hence zeros